This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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2
votes
1answer
217 views

Boundedness of expected reward Markov chain (may be related to discret $M/M/\infty$ queue)

[EDIT]: I read a bit on $M/M/\infty$ queue and it may not be the right comparison and my notation may be confusing (I'm in discrete time and $\lambda,\mu$ look likes rates when they are probability). ...
3
votes
1answer
79 views

Center of a quantum matrix algebra

Let $p \in k^\times$ be a nonroot of unity. It seems to be a well-known fact that the center of the quantum matrix algebra $\mathcal{O}_p(M_n(k))$ is generated by the quantum determinant $D_p$. It is ...
1
vote
1answer
67 views

Are there any combinatorial studies of Kirby calculus?

All of the other diagrammatic calculi I know of can be utilised with basically just combinatorial knowledge - for instance calculating knot and link polynomials. Are there similar combinatorial ...
6
votes
1answer
338 views

Book Searching in Complex Analysis

I'm searching for a problem book in complex analysis published by MIR. It was recommended by my professor (when I asked for a Demidovich equivalent in the field), but he did not remember the exact ...
18
votes
1answer
2k views

Expected rank of a random binary matrix?

Recently a friend stumbled across this question: Let $M$ be a random $n \times n$ matrix with entries in $\{0,1\}$ (both zero and one has probability $p = q = \frac{1}{2}$). What is its expected ...
1
vote
0answers
87 views

Reference request - maximum conservative extension of a probability assignment

I made up some definitions which probably lead to some interesting mathematics. However, I suspect they've studied before. So that I don't end up reinventing the wheel (always bad!), I'm after a ...
2
votes
1answer
350 views

Request for Statistics textbook

I am looking for a textbook on Statistical Analysis. Unfortunately most of the books I have seen, such as Statistics by DeGroot et al., are quite the opposite of the terse and lean textbooks I prefer ...
4
votes
2answers
154 views

Is there any wide sense but introductory Book series/websites for mathematics literature? (just to be familiar with)

Is there any Book/Book Series/Website which illustrate advanced mathematics but in concise and basic form. I just want to be familiar with the literature and I don't want a deep exploration of the ...
6
votes
1answer
405 views

How much do I need to learn before I can read about Toric varieties?

I have a copy of the book "Introduction to Toric varieties" by William Fulton, and over the next few months I'd like to make some progress on it. As a first goal, I'd like to be able to read just ...
5
votes
0answers
172 views

Coarse moduli space with no autmorphisms is also a fine moduli space

I'm working in the category of schemes over an algebraically closed field $k$, $Sch_k$. Suppose I have a contravariant functor $F:Sch_k\rightarrow (Set)$ which has a coarse moduli space $M$ (which is ...
9
votes
1answer
367 views

Emil Artin's proof for Wedderburn's Little Theorem

I am looking through different proofs for Wedderburn's Little Theorem, which states that every finite division ring is necessarily a field. I would like to read Emil Artin's proof for this theorem: ...
1
vote
1answer
163 views

What is some books at the level which including this inequality and its proof?

I always wanting to looking into harder random variable/probability/stochastic process/statistics books that are harder than the intro one and have multiple random variable but easy enough to have ...
6
votes
1answer
107 views

A new(?) partial order on the set of continuous maps

Let $X,Y$ be topological spaces. Define a partial order on $\hom(Y,X)$ as follows: $f \leq g$ if $f^{-1}(U) \subseteq g^{-1}(U)$ for all open subsets $U \subseteq X$. Equivalently, $f(y)$ is a ...
26
votes
9answers
57k views

Calculus book recommendations (for complete beginner)

Well I have not started calculus yet but I am really keen to. I would love if you suggest some books. Points to be noted: I really don't like the way textbooks are written so please no "textbooks" ...
4
votes
1answer
96 views

A property similar to countable tightness

I am interested in topological spaces having the following property: A function $f\colon X\to \mathbb R$ is continuous if and only if the restriction $f|_C$ is continuous for every countable ...
2
votes
1answer
122 views

a reference for topology [duplicate]

i am looking for a good and easy book about topology that everyone can understand it.also it be interesting.
3
votes
1answer
125 views

Good references for currents and potential theory?

I am looking for a good reference on currents and potential theory. I am already familiar with differential geometry, distribution theory and potential theory in the complex plane (at the level of the ...
1
vote
1answer
114 views

Euclidean geometry applied to Ptolemy geocentric model

I'm looking for a good reference on how Ptolemy used the Euclidean geometry to calculate the planets positions.
1
vote
1answer
186 views

Looking for friendly homework problem generator for linear algebra

Once I saw an online paper on designing friendly linear algebra problems. These would be problems where the answers use small integers or such. Now I cannot locate the paper. Any pointers?
5
votes
2answers
479 views

What is a projective ideal?

I've been looking for the definition of projective ideal but haven't found anything, all I've seen is the definition of projective module (but I don't know how these are related, if they are ¿?). Does ...
9
votes
1answer
172 views

Is this (classical?) exercice missing a hypothesis?

A friend just told me about an exercice he was given quite a few years ago, but he wasn't sure wether he remembered all the hypothesis correctly. Does anybody recognize this? Let $f$ be a smooth ...
1
vote
1answer
68 views

Reference Request: Vector Spaces

I am a new student in the field of functional analysis. I'm looking for references that make sense for all kinds of vector spaces, such as the difference between $L^2$ and $l^2$ and others like: ...
9
votes
1answer
316 views

Short and elegant introduction to Sobolev spaces

I am preparing a course on Nonlinear Analysis, and I need to teach the most important facts about Sobolev spaces to my students. I know most books on this subject, from Brezis' to Adams', from Mazya's ...
3
votes
0answers
82 views

Hyperbolic Motion in a Central Field

I have to give a 30 mins lecture this coming Thursday in my classical mechanics class (graduate level in math department, with Arnold as the primary text) and I am really struggling to find any good ...
0
votes
1answer
56 views

Theorem that stable equilibria in iterated games are equivalent to coalition-based static equilibria

Consider an $n$-player nonzero sum finite game $G$. I have a vague recollection of a wonderful paper proving an equivalence between (1) steady state Nash equilibria of $G$ played countably many times ...
7
votes
1answer
115 views

The collection of pathological examples in one reference - Reference request

I would like to ask whether there is a reference which collects pathological examples in mathematics (in general). What I mean is that, for instance, consider Weierstrass function. It has the ...
3
votes
2answers
178 views

How is “1” defined in various branches of mathematics?

Wikipedia does not elaborate much on the concept of "One" in such branches as graph theory, ring theory, algebra, topology, measure theory, formal logic, etcetera. How can one grasp the concept of ...
11
votes
2answers
827 views

Which Lie groups have Lie algebras admitting an Ad-invariant inner product?

I am trying to answer the following question: Which Lie groups have a Lie algebra admitting an $\text{Ad}$-invariant inner product? First of all, all compact Lie groups satisfy this condition ...
5
votes
2answers
3k views

Where can one find a list of prime numbers?

I am looking for the biggest list of precomputed prime numbers one can find and download. Where should I look?
2
votes
2answers
124 views

Mathematically-based online games

I am looking for online games or puzzles which have a mathematical flavor and are suitable for general audiences. A classical example is the online version of Set Card Game. Or this game that has some ...
2
votes
2answers
932 views

Reference request - Any suggestion for good Abstract Algebra pdf for computer science?

I'm a computer science student and I'm starting to learn Abstract Algebra next week. I'd like to get a suggestions for good PDF book about Abstract Algebra. Thanks!
5
votes
3answers
1k views

Is there a list of safe prime numbers?

I am looking for a list of precomputed safe prime numbers. Where can I get such a list?
7
votes
1answer
1k views

Is “Functional Analysis” by “Yosida” a good book for self study?

I was wishing to start studying by myself the book Functional Analysis by Yosida, does anyone have already used it, is it a good reference?
4
votes
1answer
496 views

Homework problems for Isaacs' Algebra: A Graduate Course?

I am about to embark on a journey through Isaacs' Algebra: A Graduate Course. He provides in the preface a very nice, detailed outline of what he covers while teaching his first-year graduate algebra ...
3
votes
0answers
101 views

Subtractive Goldbach [duplicate]

In this excellent question it occurred to me that there is a subtractive Goldbach problem: Every even integer may be written as $p-q$ for primes $p,q$. Does anyone have a reference for this problem?
7
votes
4answers
400 views

A good introduction to elementary algebra?

Is there a good book (or online text) that teaches elementary algebra? The text should focus primarily on practical computation rather than on abstract theory (while still present full proofs). For ...
1
vote
0answers
43 views

Lower bound on building heap.

A lower bound of the needed number of comparision to build a heap is given by GASTON H. GONNET and J. IAN MUNRO as following THEOREM 4. $1.3644... n + O(lg n)$ comparisons are necessary, not only ...
6
votes
6answers
4k views

Abstract algebra book recommendations for beginners.

I am taking abstract algebra in this semester. I find that my lecturer didn't provide enough examples for understanding. So I would like to ask what are the recommended books which has lots of solved ...
2
votes
1answer
872 views

How can I get a solution manual for my (abstract algebra) textbook?

I am planning to do a lot of practice excersices in algebra over the summer vacation. We are using a textbook called "Algebra" by Mark Steinberger, and so I was looking for a solution manual for this ...
10
votes
5answers
761 views

Book Recommendations and Proofs for a First Course in Real Analysis

I am taking real analysis in university. I find that it is difficult to prove some certain questions. What I want to ask is: How do we come out with a proof? Do we use some intuitive idea first and ...
24
votes
1answer
268 views

References on the theory of $2$-groups.

Many theorems about odd order $p$-groups fail miserably for $2$-groups. These can range from simple $2$-group exceptions (e.g. Frobenius complements can be either cyclic or generalized quaternion) to ...
7
votes
1answer
141 views

Is this an interesting generalization of the notion of an open set?

Let $X$ denote a topological space. Some subsets $A \subseteq X$ might have the property that $\partial A = \partial(\mathrm{int}\,A).$ This is certainly true if $A$ is open (since open implies ...
6
votes
0answers
637 views

Fun problems with binary operations.

Does anyone know of a book / internet resource containing lots of problems relating to properties of binary operations? An example of the sort of problem I'm looking for is: Let * be a binary ...
5
votes
1answer
195 views

A proof of the Weyl Character formula via fixed point formula and

I've been looking all day for a reference or notes that prove the Weyl character formula via a fixed point formula and the Borel-Weil-Bott theorem. Does anyone know of these off hand?
1
vote
0answers
53 views

spectral graph theory with “potentials”

Let G be an undirected graph with bounded degree and n vertices. Let L[G] be the corresponding graph Laplacian, which is a symmetric $n \times n$ matrix. Let V be an $n \times n$ diagonal matrix. I am ...
3
votes
1answer
70 views

Books for mathematics used in computer games.

I'm looking for a good book (idiot proof) for learning all the magic behind computing matrices, quaternions, euler angles, orientation in 3d space and more... Book needs to have examples and ...
2
votes
3answers
602 views

Mathematical applications of ordinary differential equations.

I'm looking for more mathematically oriented applications of ODEs (if possible of first order equations). I've browsed through several books and they are all full of physics applications and very ...
3
votes
0answers
114 views

The Logic of Satisfiability?

I am aware of some study into the logic of provability. It is generally taken to be intermediate in strength between S4 and S5 modal logics. Is there corresponding study into something like the logic ...
0
votes
1answer
30 views

Affects of a coordinate transformation

I am attempting to solve a PDE of $f(r,t)$, where $r\in[0,g(t)]$ is a spacial coordinate and $t$ is time. The PDE is coupled to to an ODE for $g(t)$. I wish to simplify the problem by defining a new ...
4
votes
3answers
183 views

Books about matroids

Could you recommend any approachable books/papers/texts about matroids (maybe a chapter from somewhere)? The ideal reference would contain multiple examples, present some intuitions and keep formalism ...